Diagonal of a Parallelogram Divides it into Two Congruent Triangles
Diagonal of a Parallelogram Divides it into Two Congruent Triangles
Diagonals of a Parallelogram: We know that parallelogram is a quadrilateral in which both the opposite pair of sides are parallel and equal to each other. The diagonal of a parallelogram divides it into two congruent triangles.
Theorem 1: A diagonal of a parallelogram divides it into two congruent triangles.
Given A parallelogram ABCD.
To prove A diagonal, say, AC, of parallelogram ABCD divides it into congruent triangles ABC and CDA i.e. ABC
CDA
Construction Join AC. Proof Since ABCD is a parallelogram. Therefore, AB Now, AD
Again, AB <BAC = <DCA ....(ii) [ Alternate interior angles ] Now, in <BCA = <DAC [From (i)] AC = AC [ Common side ] <BAC = <DCA [ From (i)] So, by ASA congruence criterion, we have |
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| ILLUSTRATION: Find the value of x and y in the figure | |
Solution: In the figure ABCD is a parallelogram and AC is the diagonal. We know that the diagonal of a parallelogram divides it into two congruent triangles Similarly |  |
In the following figure, ABCD is a parallelogram. The diagonal AC divides this parallelogram into which congruent triangles?
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| Right Option : B | |||
| View Explanation | |||
In the following figure, Diagonal AC divides the inner parallelogram into which two congruent triangles?
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| Right Option : C | |||
| View Explanation | |||
In the following figure, diagonal AD divides parallelogram into which two congruent triangles?
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| Right Option : B | |||
| View Explanation | |||
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Aman Kumar Shrivastava
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8thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
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Manya
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
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Ayan Ghosh
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
